Question

The fraction $\frac{x}{y}$ is altered by decreasing $x$ by $25$ per cent and increasing $y$ by $25$ percent. The new fraction is what percent less than the original?

• A. 35
• B. 40
• C. 42
• D. 45

Answer 1

The correct option is B 40

Let the fraction is $=\frac{x}{y}$

If we decrease $x$ by $25\%$, then the $x=.75x$

If we increase $y$ by $25\%$, then the $y=1.25y$

$\therefore$ new fraction is $=\frac{.75x}{1.25y}=0.6\frac{x}{y}$

So, the new fraction is $0.4$ or $40\%$ less than the original fraction.